#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
vector<vector<int>> g, b_jump;
vector<int> par, way, pos, sub;
vector<bool> ball;
int jump(int u, int h) {
if (u == -1) return 0;
if (h == 0) return u;
int x = 31 - __builtin_clz(h);
return jump(b_jump[u][x], h - (1 << x));
}
void dfs1(int u) {
sub[u] = u;
for (int h = 0; (1 << h) <= way.size(); h++) {
b_jump[u][h] = way[(int) way.size() - (1 << h)];
}
way.emplace_back(u);
for (int v: g[u]) {
dfs1(v);
sub[u] = min(sub[u], sub[v]);
}
way.pop_back();
}
void dfs2(int u) {
for (int v: g[u]) {
dfs2(v);
}
way.emplace_back(u);
}
int main() {
ios_base::sync_with_stdio(false); cin.tie(nullptr);
int n, q, h = 0;
cin >> n >> q;
while ((1 << h) < n) h++;
b_jump.assign(n + 1, vector<int>(h + 1, -1));
g.assign(n + 1, {});
par.assign(n + 1, 0);
ball.assign(n + 1, false);
sub.assign(n + 1, 0);
pos.assign(n + 1, 0);
for (int i = 1; i <= n; i++) {
cin >> par[i];
g[par[i]].emplace_back(i);
}
way.clear();
dfs1(0);
for (int i = 1; i <= n; i++) {
sort(g[i].begin(), g[i].end(), [&](int u, int v) {
return sub[u] < sub[v];
});
}
way.clear();
dfs2(0);
set<pair<int, int>> emp;
for (int i = 0; i < n; i++) {
emp.insert({i, way[i]});
pos[way[i]] = i;
}
while (q--) {
int t, x;
cin >> t >> x;
if (t == 1) {
int i = 0, last = 0;
vector<pair<int, int>> del;
for (auto it = emp.begin(); i < x; i++, it++) {
last = (*it).second;
ball[(*it).second] = true;
del.push_back(*it);
}
for (auto it: del) {
emp.erase(it);
}
cout << last << '\n';
} else {
int l = 0, r = n - 1, best = -1;
while (l <= r) {
int m = (l + r) >> 1;
int u = jump(x, m);
if (ball[u] and !ball[par[u]]) {
best = m;
break;
}
if (ball[par[u]]) {
l = m + 1;
} else {
r = m - 1;
}
}
assert(best >= 0);
x = jump(x, best);
ball[x] = false;
emp.insert({pos[x], x});
cout << best << '\n';
}
}
return 0;
}
